The meeting came as Labour set out six conditions for its support for the Government's Repeal Bill, published in Westminster.
European Union (Withdrawal) Bill, to give the "Repeal Bill" its formal title, will end the jurisdiction of EU law in the UK It will also convert existing European statutes into the British law book when the UK leaves the bloc, a move intended provide continuity for businesses and to avoid a legislative black hole appearing overnight as Britain exits the EU.
Ahead of the next round of talks starting next week, Britain on Thursday published three new position papers, including one confirming that it would withdraw from the European Atomic Energy Community.
He has demanded concessions in six areas, including incorporating the charter into United Kingdom law, ensuring workers' rights in the United Kingdom do not fall behind those in the European Union, and limiting the scope of so-called "Henry VIII powers", which could allow the Government to alter legislation without full parliamentary scrutiny.
'Two more years of uncertainty feels like a long time to a child'.
He told the Guardian: "We have very serious issues with the Government's approach, and unless the Government addresses those issues, we will not be supporting the Bill".
As the United Kingdom government publishes three position papers on Thursday, along with the Brexit repeating big that will transpose all European Union law into the United Kingdom statute books.
Labour has previously said it will vote against the bill if the European Charter of Fundamental Rights is not incorporated into British law, and the Government has now confirmed it will be ditched.
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The bill has been described as a "political power grab" due to the widespread powers it hands the government to rewrite the UK's entire legal and regulatory framework without parliamentary scrutiny.
"Nobody is seeking to frustrate the process", he insisted.
"I am keen to work across party lines to do everything we can to protect these rights".
He added: "I haven't seen any evidence that the prime minister has reflected on the outcome of the general election and indicated a willingness to change her approach to Brexit".
Liberal Democrat leader Tim Farron said his party would join Labour in giving May "hell" on the bill.
But ministers are braced for a battle over provisions that give them new powers to amend the European Union laws as they are transferred without full parliamentary scrutiny. The repeal bill is the first of eight Brexit-related bills May hopes to pass this parliament.
Sir Keir said Labour would not support the Bill in its current form and demanded concessions on workers' rights, incorporation of the European Charter of Fundamental Rights into United Kingdom law, and limiting the scope of so-called "Henry VIII powers" which could allow the Government to alter legislation without full parliamentary scrutiny.